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Robust a posteriori error estimators for mixed approximation of nearly incompressible elasticity
Author(s) -
Khan Arbaz,
Powell Catherine E.,
Silvester David J.
Publication year - 2019
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6040
Subject(s) - estimator , a priori and a posteriori , compressibility , finite element method , mathematics , elasticity (physics) , norm (philosophy) , approximation error , linear elasticity , mathematical optimization , statistics , physics , mechanics , philosophy , epistemology , political science , law , thermodynamics
Summary This paper is concerned with the analysis and implementation of robust finite element approximation methods for mixed formulations of linear elasticity problems where the elastic body is almost incompressible. Several alternative a posteriori error estimators for the energy norm of the finite element error are introduced and analysed. We establish upper and lower bounds for the energy error in terms of these error estimators and show that the constants in the bounds are independent of the Lamé coefficients: The proposed estimators are robust in the incompressible limit. We also consider the requirement for pressure stabilisation when using lowest‐order conforming approximation. Computational results are presented that validate the theoretical estimates. The software used to generate these results is available online.